extract_list_param <- function(stanMod){
l <- stanMod@model_pars
x <- list(extract_param(stanMod,"lp__")) %>% setNames("lp__")
for (i in l) {
x <- c(x,list(extract_param(stanMod,i)) %>% setNames(i))
}
x <- x[-which(names(x) == c("lp__"))]
return(x)
}
cloglog <- function(theta) log(-log(1 - theta))
extract_param <- function(model=stanMod,parmeter="alpha"){
return(summary(model, par = parmeter)$summary %>% unlist()%>%as.data.frame%>%round(.,2))
}
inv.cloglog <- function(theta) 1-exp(-exp(theta))
logreg <- function(x,b0,b1,i) y=(1/(1+exp(-(b0+(b1*(x+i))))))
scientific_10 <- function(x) {
c <- scales::scientific_format()(x)
t <- gsub("1e", "10^", c)
t2 <- gsub("10\\^\\+", "10\\^", t)
str2expression(t2)}Quantifying the detection sensitivity and precision of qPCR and ddPCR mechanisms for eDNA samples
Load functions
Load libraries
library(ggplot2)
library(dplyr)
library(rstan)
library(here);options(mc.cores = parallel::detectCores())Load data
e_ddpcr <- read.csv(here('Data','ddPCR_environmental_samples.csv'))
e_qpcr <- read.csv(here('Data','qPCR_environmental_samples.csv'))
st_ddpcr <- read.csv(here('Data','ddPCR_standard_samples.csv'))
st_qpcr <- read.csv(here('Data','qPCR_standard_samples.csv'))
st_qpcr_cm <- st_qpcr %>% filter(!is.na(Ct))
e_qpcr_cm <- e_qpcr %>% filter(!is.na(Ct))
sample_metadata <- read.csv(here('Data','Sample_metadata.csv'))
stidx <- read.csv(here('Data','sample_idx.csv'))1 Probability of detection
1.1 Create stan data
stan_data_M1 <- list(
N_i = length(unique(st_qpcr$Species)),
Nq = nrow(st_qpcr),
Ndd = nrow(st_ddpcr),
i_q_idx = st_qpcr$species_idx,
i_d_idx = st_ddpcr$species_idx,
Z_qPCR = st_qpcr$pres,
Z_ddPCR = st_ddpcr$pres,
C_qPCR = log10(st_qpcr$int_concentation),
C_ddPCR = log10(st_ddpcr$int_concentation)
);str(stan_data_M1)List of 9
$ N_i : int 3
$ Nq : int 277
$ Ndd : int 247
$ i_q_idx: int [1:277] 1 1 1 1 1 1 1 1 1 1 ...
$ i_d_idx: int [1:247] 2 1 2 1 2 1 2 1 2 1 ...
$ Z_qPCR : int [1:277] 1 1 1 1 1 1 1 1 1 1 ...
$ Z_ddPCR: int [1:247] 0 1 1 1 1 1 1 1 1 1 ...
$ C_qPCR : num [1:277] 6 5 4 3 2 1 0 6 4 3 ...
$ C_ddPCR: num [1:247] -3 -3 4 4 4 4 4 4 4 4 ...initial_values <- replicate(4,list(
alpha_0 = rep(1.0, 3),
alpha_1 = rep(0.4, 3),
beta_0 = rep(2.50, 3),
beta_1 = rep(1.23, 3)
),simplify=F)1.2 The math
\[ \begin{equation} \begin{aligned} Z_{ijk} &\sim \text{Bernoulli}(\theta_{ij}) && \text{(1)} \\ \text{logit}(\theta_{ij}) &= \phi0_{i} + \phi1_{i} \times \log_{10}(C_{ij}) && \text{(2)} \end{aligned} \end{equation} \] ## The stan code
This stan code runs 2 independent logistic regression analyses (equation 1 and 2) of qPCR and ddPCR data, with separate sets of parameters (intercepts and slopes) for each technique. To ensure comparability between the parameters \(φ0_{qPCR}\), \(φ1_{qPCR}\) and \(φ0_{ddPCR}\), \(φ1_{ddPCR}\) , we adjusted \(C_{ddPCR}\) by adding 2 in stan (\(10^2\) copies/μL) since the concentration of ddPCR standards ranged from \(10^{-3}\) to \(10^4\) , while those for qPCR range from \(10^{-1}\) to \(10^6\) . The shift aligns the slope and intercept enabling to compare the two models through their parameters (\(φ0\) and \(φ1\)).
data {
//Numbers of dimentions
int Nq; // Total number of observation in qPCR standard samples
int Ndd; // Total number of observation in ddPCR standard samples
int N_i; // Number of assays in both data (qPCR and ddPCR)
//Indexes
array[Nq] int i_q_idx; // Species/assay index for qPCR
array[Ndd] int i_d_idx; // Species/assay index for ddPCR
// Data
array[Nq] int Z_qPCR; // Presence/Absence of targets in qPCR runs
array[Ndd] int Z_ddPCR; // Presence/Absence of targets in ddPCR runs
array[Nq] real C_qPCR; // Known concentration (log10) in qPCR data
array[Ndd] real C_ddPCR; // Known concentration (log10) in qPCR data
}
parameters {
vector[N_i] phi_qPCR_0; // Intercept of logistic regression for qPCR detection probability model
vector[N_i] phi_qPCR_1; // Slope of logistic regression for qPCR detection probability model
vector[N_i] phi_ddPCR_0; // Intercept of logistic regression for ddPCR detection probability model
vector[N_i] phi_ddPCR_1; // Slope of logistic regression for ddPCR detection probability model
}
transformed parameters{
vector[Nq] theta_qPCR; // probability of detection (logit-space) qPCR model
vector[Ndd] theta_ddPCR; // probability of detection (logit-space) ddPCR model
// Logistic regression for qPCR detection probability model
for (i in 1:Nq){
theta_qPCR[i] = phi_qPCR_0[i_q_idx[i]] + (phi_qPCR_1[i_q_idx[i]] * C_qPCR[i]);
}
// Logistic regression for ddPCR detection probability model
for (i in 1:Ndd){
theta_ddPCR[i] = phi_ddPCR_0[i_d_idx[i]] + (phi_ddPCR_1[i_d_idx[i]] * (C_ddPCR[i]+2));
//' Since the standards of ddPCR range from 10^-3 - 10^4 while qPCR
//' standards range from 10^-1 - 10^6 we added 2 to C_ddPCR to make the
//' parameters phi_qPCR_0 and phi_qPCR_1 comparable with phi_ddPCR_0 and phi_ddPCR_1
}
}
model {
Z_qPCR ~ bernoulli(inv_logit(theta_qPCR));
Z_ddPCR ~ bernoulli(inv_logit(theta_ddPCR));
// Priors
phi_qPCR_0 ~ normal(0, 1);
phi_qPCR_1 ~ normal(0, 1);
phi_ddPCR_0 ~ normal(0, 1);
phi_ddPCR_1 ~ normal(0, 1);
}1.3 Run stan Model
stanMod_M1 = stan(file = here('Code','Stan_qPCR_ddPCR_prob_of_det.stan'),
chains = 4,
model_name = 'qPCR_vs_ddPCR_probability_of_detection',
iter = 5000,
warmup = 2000,
init = initial_values,
data = stan_data_M1)1.4 Data for Figure 1
# Extract parameters from stan model to build the graph
mod_out <- extract_list_param(stanMod_M1)
mod_out <- mod_out[which(names(mod_out) %in% c("phi_qPCR_0","phi_qPCR_1","phi_ddPCR_0","phi_ddPCR_1"))]
# Add species names
for (i in names(mod_out)) {
mod_out[[i]] <- mod_out[[i]] %>%
cbind(.,tibble(sp_idx = 1:3, Species = c("Cod", "Herring", "Saithe")))
}
# Construct the logistic regression for qPCR probability of detection from phi_qPCR_0 & phi_qPCR_1 parameters
probability_of_detection_qpcr <-
as.data.frame(matrix(rep(seq(-3,6,by=0.1),3),ncol=1)) %>% setNames("C") %>%
mutate(Species=rep(c("Cod","Herring","Saithe"),each=nrow(.)/3)) %>%
left_join(.,mod_out$phi_qPCR_0 %>% select(Species,mean),by="Species") %>%
rename(intercept=mean) %>%
left_join(.,mod_out$phi_qPCR_1 %>% select(Species,mean),by="Species") %>%
rename(slope=mean) %>%
mutate(prob=logreg(C,intercept,slope,0))
# Construct the logistic regression for ddPCR probability of detection from alpha_0 & alpha_1 parameters
probability_of_detection_ddpcr <-
as.data.frame(matrix(rep(seq(-3,6,by=0.1),3),ncol=1)) %>% setNames("C") %>%
mutate(Species=rep(c("Cod","Herring","Saithe"),each=nrow(.)/3)) %>%
left_join(.,mod_out$phi_ddPCR_0 %>% select(Species,mean),by="Species") %>%
rename(intercept=mean) %>%
left_join(.,mod_out$phi_ddPCR_1 %>% select(Species,mean),by="Species") %>%
rename(slope=mean) %>%
mutate(prob=logreg(C,intercept,slope,2)) #added 2 to logistic regression (see why in stan model file)
# Combine the logistic regresion lines (prob of det) of both data (qPCR and ddPCR)
probability_of_detection_data <- cbind(probability_of_detection_qpcr %>% select(C,Species,prob) %>% rename(prob_q=prob),
probability_of_detection_ddpcr %>% select(prob) %>% rename(prob_dd=prob)) %>%
mutate(delta=prob_dd-prob_q)
probability_of_detection_data %>% as_tibble() %>% print(n=20)# A tibble: 273 × 5
C Species prob_q prob_dd delta
<dbl> <chr> <dbl> <dbl> <dbl>
1 -3 Cod 0.00875 0.209 0.200
2 -2.9 Cod 0.0106 0.233 0.222
3 -2.8 Cod 0.0128 0.258 0.246
4 -2.7 Cod 0.0155 0.286 0.270
5 -2.6 Cod 0.0187 0.315 0.296
6 -2.5 Cod 0.0225 0.345 0.323
7 -2.4 Cod 0.0272 0.377 0.350
8 -2.3 Cod 0.0327 0.410 0.377
9 -2.2 Cod 0.0394 0.444 0.404
10 -2.1 Cod 0.0473 0.478 0.431
11 -2 Cod 0.0568 0.512 0.456
12 -1.9 Cod 0.0680 0.547 0.479
13 -1.8 Cod 0.0812 0.581 0.500
14 -1.7 Cod 0.0967 0.614 0.517
15 -1.6 Cod 0.115 0.646 0.531
16 -1.5 Cod 0.136 0.677 0.541
17 -1.4 Cod 0.160 0.706 0.546
18 -1.3 Cod 0.188 0.734 0.547
19 -1.2 Cod 0.219 0.760 0.542
20 -1.1 Cod 0.253 0.784 0.531
# ℹ 253 more rows1.5 Plot Figure 1 - Detection probability (qPCR vs ddPCR)
source(here('Code','Surpressed','Figure_1.R'))
Figure_1
2 Quantification precision
2.1 Create stan data
stan_data_M2 <- list(
N_st_q = nrow(st_qpcr),
N_en_q = nrow(e_qpcr),
N_st_qp = nrow(st_qpcr_cm),
N_en_qp = nrow(e_qpcr_cm),
#
N_st_d = nrow(st_ddpcr),
N_en_d = nrow(e_ddpcr),
#
N_i = length(unique(st_qpcr$Species)),
N_ij = length(unique(e_ddpcr$sp_st_idx)),
#
i_qst_idx = st_qpcr$species_idx,
i_qen_idx = e_qpcr$species_idx,
ij_qen_idx = e_qpcr$sp_st_idx,
i_qst_p_idx = st_qpcr_cm$species_idx,
i_qen_p_idx = e_qpcr_cm$species_idx,
ij_qen_p_idx = e_qpcr_cm$sp_st_idx,
Z_qPCR_st = st_qpcr$pres,
Z_qPCR_en = e_qpcr$pres,
C_qPCR_st = log10(st_qpcr$int_concentation),
Y_qPCR_st = st_qpcr_cm$Ct,
Y_qPCR_en = e_qpcr_cm$Ct,
C_qPCR_st_continuous = log10(st_qpcr_cm$int_concentation),
#
W_st = st_ddpcr$Positives,
W_en = e_ddpcr$Positives,
#
U_st = st_ddpcr$Tot_drop,
U_en = e_ddpcr$Tot_drop,
#
C_ddPCR_st = log10(st_ddpcr$int_concentation),
#
i_dst_idx = st_ddpcr$species_idx,
#
i_den_idx = e_ddpcr$species_idx,
ij_den_idx = e_ddpcr$sp_st_idx
);str(stan_data_M2)List of 28
$ N_st_q : int 277
$ N_en_q : int 1379
$ N_st_qp : int 242
$ N_en_qp : int 663
$ N_st_d : int 247
$ N_en_d : int 1052
$ N_i : int 3
$ N_ij : int 343
$ i_qst_idx : int [1:277] 1 1 1 1 1 1 1 1 1 1 ...
$ i_qen_idx : int [1:1379] 1 1 1 1 2 2 2 2 1 1 ...
$ ij_qen_idx : int [1:1379] 1 1 1 1 172 172 172 172 2 2 ...
$ i_qst_p_idx : int [1:242] 1 1 1 1 1 1 1 1 1 1 ...
$ i_qen_p_idx : int [1:663] 1 1 1 2 2 1 2 2 2 2 ...
$ ij_qen_p_idx : int [1:663] 1 1 2 173 173 3 174 175 175 175 ...
$ Z_qPCR_st : int [1:277] 1 1 1 1 1 1 1 1 1 1 ...
$ Z_qPCR_en : int [1:1379] 1 1 0 0 0 0 0 0 0 0 ...
$ C_qPCR_st : num [1:277] 6 5 4 3 2 1 0 6 4 3 ...
$ Y_qPCR_st : num [1:242] 17.2 20.3 24.3 26.9 30.7 ...
$ Y_qPCR_en : num [1:663] 43.9 46.2 49.6 40.6 40.4 ...
$ C_qPCR_st_continuous: num [1:242] 6 5 4 3 2 1 0 6 4 3 ...
$ W_st : int [1:247] 0 1 20070 20292 19709 19933 19559 19757 19520 19679 ...
$ W_en : int [1:1052] 0 0 0 0 0 0 0 0 3 2 ...
$ U_st : int [1:247] 20155 20155 20299 20299 19939 19939 19760 19760 19691 19691 ...
$ U_en : int [1:1052] 18263 18727 18377 18263 18727 18377 18711 18411 17584 18711 ...
$ C_ddPCR_st : num [1:247] -3 -3 4 4 4 4 4 4 4 4 ...
$ i_dst_idx : int [1:247] 2 1 2 1 2 1 2 1 2 1 ...
$ i_den_idx : int [1:1052] 1 1 1 2 2 2 1 1 1 2 ...
$ ij_den_idx : int [1:1052] 1 1 1 172 172 172 2 2 2 173 ...initial_values <- replicate(4,list(
kappa_0 = rep(-11, 3),
kappa_1 = rep(0.48, 3)
),simplify=F)2.2 The math
\[ \begin{aligned} &\text{qPCR model}\\ Z_{ijk} &\sim \text{Bernoulli}(\theta_{ij}) && \text{(1)} \\ \text{logit}(\theta_{ij}) &= \phi0_{i} + \phi1_{i} \times \log_{10}(C_{ij}) && \text{(2)} \\ Y_{ijk} &\sim \text{Normal}(\mu_{ij}, \sigma_{ij}) && \text{(3)} \\ \mu_{ij} &= \beta0_{i} + \beta1_{i} \times \log_{10}(C_{ij}) && \text{(4)} \\ \sigma_{ij} &= e^{(\gamma0_{i} + \gamma1_{i} \times \log_{10}(C_{ij}))} && \text{(5)} \\ \\ &\text{ddPCR model}\\ W_{ijk} &\sim \text{Binomial}(\omega_{ij}, U_{ijk}) && \text{(6)} \\ \text{cloglog}(\omega_{ij}) &= \kappa0_{i} + \kappa1_{i} \times \log_{10}(C_{ij}) && \text{(7)} \end{aligned} \] ## The stan code This stan code runs 2 independent models (equation 1 - 5 and 6 - 7) for qPCR and ddPCR data. Both models are run simultaneously for standard and environmental samples where the known concentration from standards informs the intercept and the slope parameters which thereafter informs the initial concentration of unknown samples (C).
data {
//Numbers of dimensions
// // // qPCR
int N_st_q; // Total number of observation in qPCR standard samples
int N_en_q; // Total number of observation in qPCR environmental samples
int N_st_qp; // Total number of observation in qPCR standard samples for only detected samples
int N_en_qp; // Total number of observation in qPCR environmental samples for only detected samples
// // // ddPCR
int N_st_d; // Total number of observation in ddPCR standard samples
int N_en_d; // Total number of observation in qPCR environmental samples
// // Joined
int N_i; // Number of species in both data
int N_ij; // Number of species and stations in both data
//
//Indexes
// // qPCR
// // // Binomial model
array[N_st_q] int i_qst_idx; // Species index for qPCR standard samples
array[N_en_q] int i_qen_idx; // Species index for qPCR environmental samples
array[N_en_q] int ij_qen_idx; // Species and standard index for qPCR environmental samples
// // // Continious model
array[N_st_qp] int i_qst_p_idx; // Species index for qPCR standard samples
array[N_en_qp] int i_qen_p_idx; // Species index for qPCR environmental samples
array[N_en_qp] int ij_qen_p_idx; // Species and standard index for qPCR environmental samples
// // ddPCR
array[N_st_d] int i_dst_idx; // Species index for ddPCR environmental samples
array[N_en_d] int i_den_idx; // Species index for ddPCR standard samples
array[N_en_d] int ij_den_idx; // Species and standard index for ddPCR environmental samples
//
// Data
// // qPCR
// // // Binomial model
array[N_st_q] int Z_qPCR_st; // Presence/Absence response of qPCR standard data
array[N_en_q] int Z_qPCR_en; // Presence/Absence response of qPCR environmental data
array[N_st_q] real C_qPCR_st; // Known concentration (log10) in qPCR data
// // // Continuous model
array[N_st_qp] real Y_qPCR_st; // Ct values of qPCR standard data for only detected samples
array[N_en_qp] real Y_qPCR_en; // Ct values of qPCR environmental data for only detected samples
array[N_st_qp] real C_qPCR_st_continuous; // Known concentration (log10) in qPCR data for only detected samples
// // ddPCR
array[N_st_d] int W_st; // Observed positive droplets in ddPCR standard samples
array[N_en_d] int W_en; // Observed positive droplets in ddPCR environmental samples
array[N_st_d] int U_st; // Total droplets in ddPCR standard samples
array[N_en_d] int U_en; // Total droplets in ddPCR environmental samples
array[N_st_d] real C_ddPCR_st; // Known concentration (log10) in ddPCR data
}
parameters {
// Parameters
// // qPCR
// // // Bernoulli model
vector[N_i] phi_0;
vector[N_i] phi_1;
// // // Continous model
vector[N_i] beta_0;
vector[N_i] beta_1;
vector[N_i] gamma_0;
vector<upper=0>[N_i] gamma_1;
vector[N_ij] C_qPCR;
// // ddPCR
vector[N_i] kappa_0;
vector[N_i] kappa_1;
vector<lower=-7>[N_ij] C_ddPCR;
}
transformed parameters{
// Parameters
// // qPCR
// // // Bernoulli model
vector[N_st_q] theta_st;
vector[N_en_q] theta_un;
// // // Continuous model
vector[N_st_qp] mu_st;
vector[N_en_qp] mu_en;
vector[N_st_qp] sigma_st;
vector[N_en_qp] sigma_en;
// // ddPCR
vector[N_st_d] omega_st;
vector[N_en_d] omega_en;
vector[N_ij] delta; // Difference between ddPCR and qPCR concentration estimates
//
// Model TP
// // qPCR model
// // // Bernuli module model compartment
// // // // // Standard
for (i in 1:N_st_q){
theta_st[i] = phi_0[i_qst_idx[i]] + (phi_1[i_qst_idx[i]] * C_qPCR_st[i]);
}
// // // // // Unknown (Env samples)
for (i in 1:N_en_q){
theta_un[i] = phi_0[i_qen_idx[i]] + (phi_1[i_qen_idx[i]] * C_qPCR[ij_qen_idx[i]]);
}
// // // Continuous model compartment
// // // // Standard
for (i in 1:N_st_qp){
mu_st[i] = beta_0[i_qst_p_idx[i]] + (beta_1[i_qst_p_idx[i]] * C_qPCR_st_continuous[i]);
sigma_st[i] = exp(gamma_0[i_qst_p_idx[i]]+(gamma_1[i_qst_p_idx[i]] * C_qPCR_st_continuous[i]));
}
// // // // Unknown (Env samples)
for (i in 1:N_en_qp){
mu_en[i] = beta_0[i_qen_p_idx[i]] + (beta_1[i_qen_p_idx[i]] * C_qPCR[ij_qen_p_idx[i]]);
sigma_en[i] = exp(gamma_0[i_qen_p_idx[i]]+(gamma_1[i_qen_p_idx[i]] * C_qPCR[ij_qen_p_idx[i]]));
}
// ddPCR Model
// // Standard
for (i in 1:N_st_d){
omega_st[i] = kappa_0[i_dst_idx[i]]+(kappa_1[i_dst_idx[i]]*C_ddPCR_st[i]);
}
// // // Unknown (Env samples)
for (i in 1:N_en_d){
omega_en[i] = kappa_0[i_den_idx[i]]+(kappa_1[i_den_idx[i]]*C_ddPCR[ij_den_idx[i]]);
}
for (i in 1:N_ij){
delta[i] = C_ddPCR[i]-C_qPCR[i];
}
}
model {
// Model
// // qPCR
// // // Bernoulli model
Z_qPCR_st ~ bernoulli(inv_logit(theta_st)); //Standards
Z_qPCR_en ~ bernoulli(inv_logit (theta_un)); //Unknown (Env samples)
// // // Continuous (Ct) model compartment
Y_qPCR_st ~ normal(mu_st,sigma_st);//Standards
Y_qPCR_en ~ normal(mu_en,sigma_en);//Unknown (Env samples)
// // // ddPCR
W_st ~ binomial(U_st, inv_cloglog(omega_st)); //Standards
W_en ~ binomial(U_en, inv_cloglog(omega_en)); //Unknown (Env samples)
//
// Priors
// // qPCR
// // // Bernoulli model
phi_0 ~ normal(0, 2);
phi_1 ~ normal(0, 2);
// // // Continuous model
beta_0 ~ normal(0, 3);
beta_1 ~ normal(-3, 0.1);
gamma_0 ~ normal(0, 0.1);
gamma_1 ~ normal(-1, 0.1);
C_qPCR ~ normal(0,3);
// // ddPCR
kappa_0 ~ normal(0, 1);
kappa_1 ~ normal(0, 1);
C_ddPCR ~ normal(0,3);
}2.3 Run stan Model
stanMod_M2 = stan(file = here('Code','Stan_qPCR_ddPCR_quantification_precision.stan'),chains = 4,
model_name='qPCR_vs_ddPCR_quantification_precision.stan',
iter = 5000,
warmup = 2000,
init = initial_values,
data = stan_data_M2)2.4 Data for Figure 2
# Extract DNA concentration estimation from qPCR model
q <- extract_param(stanMod_M2,"C_qPCR")
# Extract DNA concentration estimation from ddPCR model
d <- extract_param(stanMod_M2,"C_ddPCR")
# Combine the data together
diff <-
d %>% select(mean,`2.5%`,`97.5%`) %>% setNames(c("C_d","d2","d98")) %>%
cbind(.,q %>% select(mean,`2.5%`,`97.5%`) %>% setNames(c("C_q","q2","q98"))) %>%
cbind(.,e_ddpcr %>% filter(!duplicated(sp_st_idx)) %>% arrange(sp_st_idx))2.5 Plot Figure 2 - Quantification precision (qPCR vs ddPCR)
source(here('Code','Surpressed','Figure_2.R'))
Figure_2
3 Two-step model
3.1 Create stan data
# Remove an outlier that has an influence on posteriors
e_qpcr_cm <- e_qpcr_cm %>%
filter(!(Well=="A4"&
Sample_name=="2021624_10"&
Species =="Herring"&
Ct==42.56510544&
Conc==0.139179796&
plate=="Plate_G"))
stan_data_M3 <- list(
N_st_q = nrow(st_qpcr),
N_en_q = nrow(e_qpcr),
N_st_qp = nrow(st_qpcr_cm),
N_en_qp = nrow(e_qpcr_cm),
#
N_st_d = nrow(st_ddpcr),
N_en_d = nrow(e_ddpcr),
#
N_i = length(unique(st_qpcr$Species)),
N_ij = length(unique(e_ddpcr$sp_st_idx)),
#
i_qst_idx = st_qpcr$species_idx,
i_qen_idx = e_qpcr$species_idx,
ij_qen_idx = e_qpcr$sp_st_idx,
#
i_qst_p_idx = st_qpcr_cm$species_idx,
i_qen_p_idx = e_qpcr_cm$species_idx,
ij_qen_p_idx = e_qpcr_cm$sp_st_idx,
#
Z_qPCR_st = st_qpcr$pres,
Z_qPCR_en = e_qpcr$pres,
C_qPCR_st = log10(st_qpcr$int_concentation),
#
Y_qPCR_st = st_qpcr_cm$Ct,
Y_qPCR_en = e_qpcr_cm$Ct,
C_qPCR_st_cont = log10(st_qpcr_cm$int_concentation)
);str(stan_data_M3)List of 20
$ N_st_q : int 277
$ N_en_q : int 1379
$ N_st_qp : int 242
$ N_en_qp : int 662
$ N_st_d : int 247
$ N_en_d : int 1052
$ N_i : int 3
$ N_ij : int 343
$ i_qst_idx : int [1:277] 1 1 1 1 1 1 1 1 1 1 ...
$ i_qen_idx : int [1:1379] 1 1 1 1 2 2 2 2 1 1 ...
$ ij_qen_idx : int [1:1379] 1 1 1 1 172 172 172 172 2 2 ...
$ i_qst_p_idx : int [1:242] 1 1 1 1 1 1 1 1 1 1 ...
$ i_qen_p_idx : int [1:662] 1 1 1 2 2 1 2 2 2 2 ...
$ ij_qen_p_idx : int [1:662] 1 1 2 173 173 3 174 175 175 175 ...
$ Z_qPCR_st : int [1:277] 1 1 1 1 1 1 1 1 1 1 ...
$ Z_qPCR_en : int [1:1379] 1 1 0 0 0 0 0 0 0 0 ...
$ C_qPCR_st : num [1:277] 6 5 4 3 2 1 0 6 4 3 ...
$ Y_qPCR_st : num [1:242] 17.2 20.3 24.3 26.9 30.7 ...
$ Y_qPCR_en : num [1:662] 43.9 46.2 49.6 40.6 40.4 ...
$ C_qPCR_st_cont: num [1:242] 6 5 4 3 2 1 0 6 4 3 ...3.2 The math
\[ \begin{aligned} &\text{qPCR model joint}\\ Z_{ijk} &\sim \text{Bernoulli}(\theta_{ij}) && \text{(1)} \\ \text{logit}(\theta_{ij}) &= \phi0_{i} + \phi1_{i} \times \log_{10}(C_{ij}) && \text{(2)} \\ Y_{ijk} &\sim \text{Normal}(\mu_{ij}, \sigma_{ij}) && \text{(3)} \\ \mu_{ij} &= \beta0_{i} + \beta1_{i} \times \log_{10}(C_{ij}) && \text{(4)} \\ \sigma_{ij} &= e^{(\gamma0_{i} + \gamma1_{i} \times \log_{10}(C_{ij}))} && \text{(5)} \\ \\ &\text{qPCR model continuous (single)}\\ Y_{ijk} &\sim \text{Normal}(\mu_{ij}, \sigma_{ij}) && \text{(3)} \\ \mu_{ij} &= \beta0_{i} + \beta1_{i} \times \log_{10}(C_{ij}) && \text{(4)} \\ \sigma_{ij} &= e^{(\gamma0_{i} + \gamma1_{i} \times \log_{10}(C_{ij}))} && \text{(5)} \\ \end{aligned} \]
3.3 The stan code
data {
//Numbers of dimentions
// // // qPCR
int N_st_q; // Total number of observation in qPCR standard samples
int N_en_q; // Total number of observation in qPCR environmental samples
int N_st_qp; // Total number of observation in qPCR standard samples for only detected samples
int N_en_qp; // Total number of observation in qPCR environmental samples for only detected samples
// // // ddPCR
int N_en_d; // Total number of observation in qPCR environmental samples
// // Joined
int N_i; // Number of species in both data
int N_ij; // Number of species and stations in both data
//
//Indexes
// // qPCR
// // // Binomial model
array[N_st_q] int i_qst_idx; // Species index for qPCR standard samples
array[N_en_q] int i_qen_idx; // Species index for qPCR environmental samples
array[N_en_q] int ij_qen_idx; // Species and standard index for qPCR environmental samples
// // // Continious model
array[N_st_qp] int i_qst_p_idx; // Species index for qPCR standard samples
array[N_en_qp] int i_qen_p_idx; // Species index for qPCR environmental samples
array[N_en_qp] int ij_qen_p_idx; // Species and standard index for qPCR environmental samples
//
// Data
// // qPCR
// // // Binomial model
array[N_st_q] int Z_qPCR_st; // Presence/Absence response of qPCR standard data
array[N_en_q] int Z_qPCR_en; // Presence/Absence response of qPCR environmental data
array[N_st_q] real C_qPCR_st; // Known concentration (log10) in qPCR data
// // // Continious model
array[N_st_qp] real Y_qPCR_st; // Ct values of qPCR standard data for only detected samples
array[N_en_qp] real Y_qPCR_en; // Ct values of qPCR environmental data for only detected samples
array[N_st_qp] real C_qPCR_st_cont; // Known concentration (log10) in qPCR data for only detected samples
}
parameters {
// Parameters
// // qPCR
// // // Bernoulli model
vector[N_i] phi_0;
vector[N_i] phi_1;
// // // Continous model (joint)
vector[N_i] beta_joint_0;
vector[N_i] beta_joint_1;
vector[N_i] gamma_joint_0;
vector<upper=0>[N_i] gamma_joint_1;
vector[N_ij] C_qPCR_joint;
// // // Continous model (single)
vector[N_i] beta_cont_0;
vector[N_i] beta_cont_1;
vector[N_i] gamma_cont_0;
vector<upper=0>[N_i] gamma_cont_1;
vector[N_ij] C_qPCR_continuous;
}
transformed parameters{
// Parameters
// // qPCR
// // // Bernoulli model
vector[N_st_q] theta_st;
vector[N_en_q] theta_un;
// // // Continious model (joint)
vector[N_st_qp] mu_st;
vector[N_en_qp] mu_en;
vector[N_st_qp] sigma_st;
vector[N_en_qp] sigma_en;
// // // Continious model (single)
vector[N_st_qp] mu_st_nor;
vector[N_en_qp] mu_en_nor;
vector[N_st_qp] sigma_st_nor;
vector[N_en_qp] sigma_en_nor;
//
// Model TP
// // qPCR model
// // // Bernuli module model compartment
// // // // // Standard
for (i in 1:N_st_q){
theta_st[i] = phi_0[i_qst_idx[i]] + (phi_1[i_qst_idx[i]] * C_qPCR_st[i]);
}
// // // // // Unknown
for (i in 1:N_en_q){
theta_un[i] = phi_0[i_qen_idx[i]] + (phi_1[i_qen_idx[i]] * C_qPCR_joint[ij_qen_idx[i]]);
}
// // // Continious model compartment (joint)
// // // // Standard
for (i in 1:N_st_qp){
mu_st[i] = beta_joint_0[i_qst_p_idx[i]] + (beta_joint_1[i_qst_p_idx[i]] * C_qPCR_st_cont[i]);
sigma_st[i] = exp(gamma_joint_0[i_qst_p_idx[i]]+(gamma_joint_1[i_qst_p_idx[i]] * C_qPCR_st_cont[i]));
}
// // // // Unknown
for (i in 1:N_en_qp){
mu_en[i] = beta_joint_0[i_qen_p_idx[i]] + (beta_joint_1[i_qen_p_idx[i]] * C_qPCR_joint[ij_qen_p_idx[i]]);
sigma_en[i] = exp(gamma_joint_0[i_qen_p_idx[i]]+(gamma_joint_1[i_qen_p_idx[i]] * C_qPCR_joint[ij_qen_p_idx[i]]));
}
// // // Continious model compartment (single)
// // // // Standard
for (i in 1:N_st_qp){
mu_st_nor[i] = beta_cont_0[i_qst_p_idx[i]] + (beta_cont_1[i_qst_p_idx[i]] * C_qPCR_st_cont[i]);
sigma_st_nor[i] = exp(gamma_cont_0[i_qst_p_idx[i]]+(gamma_cont_1[i_qst_p_idx[i]] * C_qPCR_st_cont[i]));
}
// // // // Unknown
for (i in 1:N_en_qp){
mu_en_nor[i] = beta_cont_0[i_qen_p_idx[i]] + (beta_cont_1[i_qen_p_idx[i]] * C_qPCR_continuous[ij_qen_p_idx[i]]);
sigma_en_nor[i] = exp(gamma_cont_0[i_qen_p_idx[i]]+(gamma_cont_1[i_qen_p_idx[i]] * C_qPCR_continuous[ij_qen_p_idx[i]]));
}
}
model {
// Model
// // qPCR
// // // Bernoulli model
Z_qPCR_st ~ bernoulli(inv_logit(theta_st)); //Standards
Z_qPCR_en ~ bernoulli(inv_logit (theta_un)); //Unknown (Env samples)
// // // Continuous (Ct) model compartment (joint)
Y_qPCR_st ~ normal(mu_st,sigma_st);//Standards
Y_qPCR_en ~ normal(mu_en,sigma_en);//Unknown (Env samples)
// // // Continuous (Ct) model compartment (single)
Y_qPCR_st ~ normal(mu_st_nor,sigma_st_nor);//Standards
Y_qPCR_en ~ normal(mu_en_nor,sigma_en_nor);//Unknown (Env samples)
//
// Priors
// // qPCR
// // // Bernoulli model
phi_0 ~ normal(0, 2);
phi_1 ~ normal(0, 2);
// // // Continious model (joint)
beta_joint_0 ~ normal(0, 3);
beta_joint_1 ~ normal(-3, 0.1);
gamma_joint_0 ~ normal(0, 0.1);
gamma_joint_1 ~ normal(-1, 0.1);
C_qPCR_joint ~ normal(0,1);
// // // Continious model (single)
beta_cont_0 ~ normal(0, 3);
beta_cont_1 ~ normal(-3, 0.1);
gamma_cont_0 ~ normal(0, 0.1);
gamma_cont_1 ~ normal(-1, 0.1);
C_qPCR_continuous ~ normal(0,1);
}3.4 Run stan Model
stanMod_M3 = stan(file = here('Code','Stan_qPCR_two_step_model.stan'),
chains = 4,
model_name='qPCR_two_step_model',
iter = 5000,
warmup=2000,
data = stan_data_M3)Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
Running the chains for more iterations may help. See
https://mc-stan.org/misc/warnings.html#tail-ess3.5 Data for Figure 3
q_bin <-
extract_param(stanMod_M3,"C_qPCR_joint") %>% cbind(.,e_qpcr %>% filter(!duplicated(sp_st_idx)) %>% arrange(sp_st_idx) %>% select(-Ct,-Conc,-pres)) %>%
select(mean,`97.5%`,`2.5%`,Species) %>% setNames(c("C_qPCR_joint","q98","q2","Species")) %>%
slice(e_qpcr_cm %>% filter(!duplicated(sp_st_idx)) %>% pull(sp_st_idx) %>% sort())
q_nor <-
extract_param(stanMod_M3,"C_qPCR_continuous") %>% slice(e_qpcr_cm %>% filter(!duplicated(sp_st_idx)) %>% pull(sp_st_idx) %>% sort()) %>%
cbind(.,e_qpcr_cm %>% filter(!duplicated(sp_st_idx)) %>% arrange(sp_st_idx) %>% select(-Ct,-Conc,-pres)) %>%
select(mean,`97.5%`,`2.5%`,Species) %>% setNames(c("C_qPCR_continuous","q98","q2","Species"))
diff <- cbind(q_bin %>% setNames(c("C_qPCR_joint","q98_bin","q2_bin","Species")) %>%
select(-Species),
q_nor %>% setNames(c("C_qPCR_continuous","q98_nor","q2_nor","Species"))) %>%
mutate(diff=(q98_nor-q2_nor)-(q98_bin-q2_bin))3.6 Plot Figure 3 - Two-step qPCR model quantification precision
source(here('Code','Surpressed','Figure_3.R'))
Figure_3
4 Lower threshold
4.1 The math
\[ \begin{aligned} \log_{10}(C_{lt}) = \frac{\text{cloglog}\left(\frac{1}{U}\right) - \kappa_0}{\kappa_1} \end{aligned} \] ## Extract the data from stan Model 2
kappa_0 <- extract_param(stanMod_M2,"kappa_0") %>%
cbind(.,e_ddpcr %>%
filter(!duplicated(species_idx)) %>%
arrange(species_idx) %>%
select(Species,species_idx))
kappa_1 <- extract_param(stanMod_M2,"kappa_1") %>%
cbind(.,e_ddpcr %>%
filter(!duplicated(species_idx)) %>%
arrange(species_idx) %>%
select(Species,species_idx))nrep_st <- 1
nrep_end <- 10
repl <- rep(c(nrep_st:nrep_end),3)
minimum_threshold <- repl %>% as.data.frame() %>%
cbind(.,kappa_0 %>% pull(mean) %>% rep(.,each=nrep_end)) %>%
cbind(.,kappa_1 %>% pull(mean) %>% rep(.,each=nrep_end)) %>%
cbind(.,kappa_0 %>% pull(Species) %>% rep(.,each=nrep_end)) %>%
setNames(c("replicates","kappa_0","kappa_1","Species")) %>%
mutate(C_lt=(cloglog(1/(20000*replicates))-kappa_0)/kappa_1) %>%
mutate(C_ut=(cloglog(((20000*replicates)-1)/(20000*replicates))-kappa_0)/kappa_1)4.2 Plot Figure 4 - ddPCR minimum threshold
source(here('Code','Surpressed','Figure_4.R'))
Figure_4
5 Supplementary plots
Load additional data
qpcr_optimisation_cod_herring_plate <- read.csv(here('Data','qPCR_opt_Cod_Herring.csv'))
qpcr_optimisation_cod_saithe_plate <- read.csv(here('Data','qPCR_opt_Cod_Saithe.csv'))
ddpcr_amplitude_cod_herring_standard_samples <- read.csv(here('Data','ddpcr_amplitude_cod_herring_standard_samples.csv'))
ddpcr_amplitude_cod_saithe_standard_samples <- read.csv(here('Data','ddpcr_amplitude_cod_saithe_standard_samples.csv'))5.1 Figure S1 - Optimization of qPCR plates
opt_dat <- rbind(qpcr_optimisation_cod_saithe_plate,
qpcr_optimisation_cod_herring_plate) %>%
filter(SuperMix!="OUT") %>%
mutate(Conc=if_else(Sample=="ST1",6,0)) %>%
mutate(Conc=if_else(Sample=="ST3",4,Conc)) %>%
mutate(Conc=if_else(Sample=="ST5",2,Conc)) %>%
mutate(Conc=if_else(Sample=="Blank",-Inf,Conc)) %>%
mutate(SM=substr(SuperMix,start = 3,stop = 3))
pp1 <-
opt_dat %>% filter(Conc!=-Inf) %>%
ggplot(aes(x=SM,y=Ct,color=Species))+
geom_boxplot()+
theme_bw()+
facet_wrap(~Conc ~ Species,scales="free_y",ncol=3,
labeller=label_bquote(cols = 10 ^ .(Conc) ~ "(copies/µL)"))+
scale_color_manual(values=c("tomato2", "deepskyblue2","orange2"))+
ylab("Cycle threshold (Ct)")+
xlab("SuperMix (SM)")+
theme(legend.position = "none",
strip.background = element_blank(),
strip.text.x = element_text(size=17),
axis.title.y = element_text(size = 19),
plot.margin = margin(0.1, 0.1, 0.5, 0.5, "cm"),
axis.title.x = element_text(size = 19),
axis.text.x = element_text(size=15),
axis.text.y=element_text(size=15))
p1_leg <-
opt_dat %>% filter(SuperMix!="OUT"&Conc!=-Inf) %>%
ggplot(aes(x=SuperMix,y=Ct,color=Species))+
geom_boxplot()+
theme_bw()+
scale_color_manual(values=c("tomato2", "deepskyblue2","orange2"))+
theme(legend.title = element_text(size = 20),
legend.text = element_text(size = 16)) # Adjust the size as needed
mat <- matrix(paste0("SM", c(1:3,5:7,9,8,4)), nrow = 3, byrow = TRUE)
df <- expand.grid(row = 1:3, col = 1:3)
df$label <- as.vector(mat)
df$F_p <- rep(c(2.5,10,17),3)
df$R_p <- rep(c(2.5,10,17),each=3)
pp2 <-
ggplot(df, aes(x = col, y = row, label = label, fill = label)) +
geom_tile(color = "white", size = 1) +
geom_text(size = 5, color = "black") +
geom_text(aes(x = 0.2, y = row, label = F_p), hjust = 0.1,size=5) +
geom_text(aes(x = col, y = 0.15, label = R_p), vjust = -0.5,size=5) +
scale_fill_manual(values = rep("grey", 9)) +
ggtitle("SuperMix (SM) \nconcentration") + # Add your desired title here
theme_minimal() +
ylab("Forward primer \nconcentration (nM)")+
xlab("Reverse primer \nconcentration (nM)")+
theme(
legend.position = "none",
axis.title.y = element_text(size = 14),
axis.title.x = element_text(size = 14),
axis.title = element_blank(),
plot.margin = margin(1, 0, 0.1, 0.5, "cm"),
axis.text = element_blank(),
axis.ticks = element_blank(),
panel.grid = element_blank(),
plot.title = element_text(hjust = 0.5,size = 20)
)
p1_leg_leg <- cowplot::get_legend(p1_leg+
theme(legend.justification = c(0.4,0.0)))
p1 <-
cowplot::plot_grid(p1_leg_leg,pp2, nrow = 3)
Figure_S1 <- cowplot::plot_grid(pp1,p1,rel_widths = c(5,1.5))Figure_S1
5.2 Figure S2 - ddPCR droplet proportion
pp1 <-
ggplot(data=st_ddpcr %>%
group_by(Sample_name, Species) %>%
summarise(nominal_c = mean(int_concentation),
pos_agg = sum(Positives),
tot_agg = sum(Tot_drop),
sp_idx = mean(species_idx),
Conc = mean(Conc))) +
geom_point(aes(x=Conc, y=cloglog(pos_agg/tot_agg),
color=Species),size=2)+
geom_point(aes(x=nominal_c, y=cloglog(pos_agg/tot_agg),
color=Species),shape=23,size=2)+
geom_smooth(aes(x=Conc, y=cloglog(pos_agg/tot_agg),
color=Species),
method=lm, se=F, fullrange=T,lty=3,size=0.5)+
stat_smooth(aes(x=nominal_c, y=cloglog(pos_agg/tot_agg),
color=Species),
method = lm, formula = y ~ poly(x, 3),lty=1,size=0.5, se=F)+
theme_bw()+
scale_color_manual(values=c("tomato2", "deepskyblue2","orange2"))+
facet_grid(~Species)+
scale_x_log10(labels=scientific_10,lim=c(1e-3,1e5),breaks=c(10^seq(-3,5,by=2)))+
theme(legend.position = "none",
strip.background = element_blank(),
strip.text.x = element_blank(),
axis.title.y = element_text(size = 19),
plot.margin = margin(0.1, 0, 0.3, 0, "cm"),
axis.title.x = element_text(size = 19),
axis.text.x = element_text(size = 15),
axis.text.y=element_text(size=15))+
ylab(expression(atop("cloglog("*omega*")",paste(omega*" = positive droplets / total droplets"))))+
xlab("Nominal concentration (copies/µL)")
p1_leg <- ggplot() +
geom_point(aes(x = NA, y = NA, color = "Gadus morhua"), size = 1) +
geom_point(aes(x = NA, y = NA, color = "Clupea harengus"), size = 1) +
geom_point(aes(x = NA, y = NA, color = "Pollachius virens"), size = 1) +
geom_line(aes(x = NA, y = NA, color = "Gadus morhua"), size = 1) +
geom_line(aes(x = NA, y = NA, color = "Clupea harengus"), size = 1) +
geom_line(aes(x = NA, y = NA, color = "Pollachius virens"), size = 1) +
theme_bw()+
scale_color_manual(
name='Assay',
breaks=c("Gadus morhua", "Clupea harengus","Pollachius virens"),
values = c("tomato2", "deepskyblue2","orange"),
guide = guide_legend(
override.aes = list(lty = c(1,1,1),
size = c(3,3,3)))) +
theme(plot.margin = margin(1, 4, 1, 0, "cm"),
legend.key.width = unit(1.2,"cm"),
legend.title = element_text(size=18),
legend.key.height = unit(0.8, 'cm'),
legend.text = element_text(size=16,face = "italic"))
p1_leg_leg <- cowplot::get_legend(p1_leg+
theme(legend.justification = c(0,0.0)))
p2_leg <- ggplot() +
geom_line(aes(x = NA, y = NA, color = "ddPCR (in-built estimation)"),size = 1) +
geom_line(aes(x = NA, y = NA, color = "Nominal concentration"), size = 1) +
geom_point(aes(x = NA, y = NA, color = "ddPCR (in-built estimation)"), size = 1,shape=23) +
geom_point(aes(x = NA, y = NA, color = "Nominal concentration"), size = 1) +
theme_bw()+
scale_color_manual(
name='Method of measurement',
breaks=c("ddPCR (in-built estimation)","Nominal concentration"),
values = c("black","black"),
guide = guide_legend(
override.aes = list(lty = c(3,1),
size = c(3,3),
shape= c(19,23)))) +
theme(plot.margin = margin(1, 0.1, 0, 0, "cm"),
legend.key.width = unit(1.2,"cm"),
legend.title = element_text(size=18),
legend.key.height = unit(0.8, 'cm'),
legend.text = element_text(size=16))
p2_leg_leg <- cowplot::get_legend(p2_leg+
theme(legend.justification = c(0,1.0)))
legend <- cowplot::plot_grid(p1_leg_leg, p2_leg_leg, nrow = 2)
Figure_S2 <- cowplot::plot_grid(pp1,legend,nrow=1,rel_widths = c(4,1.1))Figure_S2
5.3 Figure S3 - Possion statistics between assays
kappa_0 <- extract_param(stanMod_M2,"kappa_0") %>%
cbind(.,e_ddpcr %>%
filter(!duplicated(species_idx)) %>%
arrange(species_idx) %>%
select(Species,species_idx))
kappa_1 <- extract_param(stanMod_M2,"kappa_1") %>%
cbind(.,e_ddpcr %>%
filter(!duplicated(species_idx)) %>%
arrange(species_idx) %>%
select(Species,species_idx))
conc_st <- -2
conc_end <- 5
repl <- rep(seq(conc_st,conc_end,by=0.1),3)
logist_diff <-
repl %>% as.data.frame() %>%
cbind(.,kappa_0 %>% pull(mean) %>% rep(.,each=length(repl)/3)) %>%
cbind(.,kappa_1 %>% pull(mean) %>% rep(.,each=length(repl)/3)) %>%
cbind(.,kappa_0 %>% pull(Species) %>% rep(.,each=length(repl)/3)) %>%
setNames(c("C","intercept","slope","Species")) %>%
mutate(omega=intercept+(slope*C))
sim <- seq(-2,4.9,by=0.1) %>% as.data.frame() %>% setNames("C") %>%
mutate(omega=inv.cloglog(-7.07+(2.3*C)))
pp1 <-
logist_diff %>%
ggplot()+
geom_line(aes(y=inv.cloglog(omega),x=10^C,color=Species),lwd=1)+
geom_line(data=sim,aes(y=(omega),x=10^C),color="black",lty=2,lwd=0.3)+
scale_x_log10(labels=scientific_10,breaks=c(10^seq(conc_st,conc_end)))+ #
scale_y_sqrt()+
scale_color_manual(values=c("tomato2", "deepskyblue2","orange2"))+
theme_bw()+
theme(legend.position = "none",
strip.background = element_blank(),
strip.text.x = element_blank(),
axis.title.y = element_text(size = 19),
plot.margin = margin(0.1, 0.1, 0.5, 0.5, "cm"),
axis.title.x = element_text(size = 19),
axis.text.x = element_text(size=14),
axis.text.y=element_text(size=14))+
ylab(expression("Proportion of positive droplets"))+
xlab("Nominal concentration (copies/µL)")
p1_leg <- ggplot() +
geom_line(aes(x = NA, y = NA, color = "Gadus morhua"), size = 1) +
geom_line(aes(x = NA, y = NA, color = "Clupea harengus"), size = 1) +
geom_line(aes(x = NA, y = NA, color = "Pollachius virens"), size = 1) +
theme_bw()+
scale_color_manual(
name='Bayesian estimated\nassay',
breaks=c("Gadus morhua", "Clupea harengus","Pollachius virens"),
values = c("tomato2", "deepskyblue2","orange"),
guide = guide_legend(
override.aes = list(lty = c(1,1,1),
size = c(2,2,2)))) +
theme(plot.margin = margin(1, 4, 1, 0, "cm"),
legend.key.width = unit(1.2,"cm"),
legend.title = element_text(size=18),
legend.key.height = unit(0.8, 'cm'),
legend.text = element_text(size=16,face = "italic"))
p1_leg_leg <- cowplot::get_legend(p1_leg+
theme(legend.justification = c(0,0.1)))
p2_leg <- ggplot() +
geom_line(aes(x = NA, y = NA, color = "ddPCR (in-built estimation)"), size = 1) +
theme_bw()+
scale_color_manual(
name='Poisson statistics',
breaks=c("ddPCR (in-built estimation)"),
values = c("black"),
guide = guide_legend(
override.aes = list(lty = c(2),
size = c(1)))) +
theme(plot.margin = margin(1, 4, 1, 0, "cm"),
legend.key.width = unit(1.2,"cm"),
legend.title = element_text(size=18),
legend.key.height = unit(0.8, 'cm'),
legend.text = element_text(size=16,face = "italic"))
p2_leg_leg <- cowplot::get_legend(p2_leg+
theme(legend.justification = c(0,1.0)))
legend <- cowplot::plot_grid(p1_leg_leg,p2_leg_leg,nrow = 2)
Figure_S3 <- cowplot::plot_grid(pp1,legend,nrow=1,ncol=2,rel_widths = c(4,1.3))Figure_S3
5.4 Figure S4 - Assay performance amplitude
amp_dat <- rbind(ddpcr_amplitude_cod_herring_standard_samples,
ddpcr_amplitude_cod_saithe_standard_samples)
pp1 <-
amp_dat %>%
ggplot() +
geom_jitter(aes(y=MeanAmplitudeOfPositives,x=Species,shape = assay),size=2,color="forestgreen")+
geom_boxplot(aes(x = Species, y = MeanAmplitudeOfPositives),fill="forestgreen",
alpha=0.5)+
geom_jitter(aes(y=MeanAmplitudeOfNegatives,x=Species,shape = assay),size=2,color="tomato2")+
geom_boxplot(aes(x = Species, y = MeanAmplitudeOfNegatives),fill="tomato2",
alpha=0.5)+
theme_bw()+
scale_shape_manual(values = c(17, 19)) +
labs(x = "Species",
y = "Mean amplitude of droplets")+
theme(legend.position = "none",
strip.background = element_blank(),
strip.text.x = element_blank(),
axis.title.y = element_text(size = 22),
axis.title.x = element_text(size = 22),
plot.margin = margin(0.1, 0.1, 0.5, 0.5, "cm"),
axis.text.x = element_text(size=18),
axis.text.y=element_text(size=16))
p1_leg <-
ggplot() +
geom_point(aes(x = NA, y = NA, color = "Positive droplet"), size = 1) +
geom_point(aes(x = NA, y = NA, color = "Negative droplet"), size = 1) +
theme_bw()+
scale_color_manual(
name='Detection',
breaks=c("Positive droplet", "Negative droplet"),
values = c("forestgreen", "tomato2"),
guide = guide_legend(
override.aes = list(lty = c(1,1),
size = c(2,2)))) +
theme(plot.margin = margin(1, 4, 1, 0, "cm"),
legend.key.width = unit(1.2,"cm"),
legend.title = element_text(size=18),
legend.key.height = unit(0.8, 'cm'),
legend.text = element_text(size=16))
p2_leg <-
ggplot() +
geom_point(aes(x = NA, y = NA, color = "Cod + herring"), size = 1) +
geom_point(aes(x = NA, y = NA, color = "Cod + saithe"), size = 1) +
theme_bw()+
scale_color_manual(
name="Assay",
breaks=c("Cod + herring", "Cod + saithe"),
values = c("black", "black"),
guide = guide_legend(
override.aes = list(shape = c(17,19),
size = c(2,2)))) +
theme(plot.margin = margin(1, 4, 1, 0, "cm"),
legend.key.width = unit(1.2,"cm"),
legend.title = element_text(size=18),
legend.key.height = unit(0.8, 'cm'),
legend.text = element_text(size=16))
p1_leg_leg <- cowplot::get_legend(p1_leg+
theme(legend.justification = c(0,0.0)))
p2_leg_leg <- cowplot::get_legend(p2_leg+
theme(legend.justification = c(0,1.0)))
legend <- cowplot::plot_grid(p1_leg_leg,p2_leg_leg,nrow = 2)
Figure_S4 <- cowplot::plot_grid(pp1,legend,ncol = 2, rel_widths = c(4,1))Figure_S4
5.5 Figure S5 - LoD and LoQ
# Filter out 2 outliers
DAT <- st_qpcr %>%
filter(!(Well=='B2'&Ct==16.80747223)) %>%
filter(!(Well=='G1'&Ct==44.88344574))
source(here('Code','Surpressed','Figure_S5_LoD_LoQ.R'))Figure_S5